Electrically tunable continuous-time circuit and method for compensating a polynomial voltage-dependent characteristic of capacitance

ABSTRACT

A capacitance compensation circuit includes an input terminal, a plurality of switches coupled to the input terminal, a plurality of varactors coupled to the plurality of switches, and a plurality of blocking capacitors coupled between the plurality of switches and the plurality of varactors. The capacitance compensation circuit further includes a plurality of adjustable biasing circuits to precisely compensate for linear and parabolic voltage dependent components of an input or other capacitor. Two such circuits can be used with a single input terminal to compensate for both increasing and decreasing voltage dependent characteristics of a target capacitor.

RELATED APPLICATIONS

The present application is related to my co-pending applicationentitled, “Continuous-Time Circuit and Method for CapacitanceEqualization Based on Electrically Tunable Voltage Pre-Distortion of aC-V Characteristic”, U.S. patent application Ser. No. 12/775,381, filedMay 6, 2010, which is hereby incorporated in its entirety by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates, in general, to capacitance compensationcircuits, and, more particularly, to a continuous-time circuit andmethod for compensating a polynomial voltage-dependent characteristic ofa capacitor.

2. Relevant Background

Input-dependent capacitance constitutes one of the main limitations tothe ideality of a radio-frequency (RF) as well as of an analog precisionfront-end. In fact, traditionally even necessary structures such asElectro-Static Discharge (ESD) protection diodes and other clampingcircuitry have been minimized at the very input of those circuits, totry and mitigate the distortion effects caused by input-dependentcapacitance. While the solution of minimizing the input structures maylessen the undesirable effect of input-dependent capacitance, it is notalways practical depending on the specific application, nor does itsubstantially eliminate distortion. For extremely high precisioncircuits targeting 100 dB of dynamic range and higher, even the smallamount of remaining input-dependent capacitance must be addressed. Thus,a need remains for a compensation circuit that can be adjusted tocorrect for the voltage-dependency in an input capacitor.

SUMMARY OF THE INVENTION

According to a first embodiment of the present invention, a capacitancecompensation circuit includes an input terminal, a plurality of switchescoupled to the input terminal, a plurality of varactors coupled to theplurality of switches, and a plurality of blocking capacitors coupledbetween the plurality of switches and the plurality of varactors. Thecapacitance compensation circuit further includes a plurality ofadjustable biasing circuits to precisely compensate for linear andparabolic voltage dependent components of an input or other capacitor.

According to a second embodiment of the present invention, a capacitancecompensation circuit includes a first circuit to compensate for inputcapacitance increasing against the input terminal voltage, including afirst plurality of switches coupled to the input terminal, a firstplurality of blocking capacitors coupled to the first plurality ofswitches, and a first plurality of varactors coupled to the plurality ofblocking capacitors; and a second circuit to compensate for inputcapacitance decreasing against the input terminal voltage, including asecond plurality of switches coupled to the input terminal, a secondplurality of blocking capacitors coupled to the second plurality ofswitches, and a second plurality of varactors coupled to the secondplurality of blocking capacitors. The first and second circuit eachinclude a plurality of adjustable biasing circuits to preciselycompensate for linear and parabolic voltage dependent components of aninput or other capacitor.

According to a third embodiment of the present invention, a capacitancecompensation circuit includes a first plurality of varactors coupled tothe input terminal, and a second plurality of varactors coupled to thefirst plurality of varactors at a plurality of intermediate nodes. Thecircuit includes a plurality of adjustable biasing circuits to preciselycompensate for linear and parabolic voltage dependent components of aninput or other capacitor.

According to a fourth embodiment of the present invention, a capacitancecompensation circuit includes a first circuit portion including a firstplurality of varactors coupled to the input terminal and a secondplurality of varactors coupled to the first plurality of varactors at afirst plurality of intermediate nodes, and a second circuit portionincluding a third plurality of varactors coupled to the input terminaland a fourth plurality of varactors coupled to the third plurality ofvaractors at a second plurality of intermediate nodes. The first andsecond circuit portions each include a plurality of adjustable biasingcircuit to precisely compensate for linear and parabolic voltagedependent components of an input or other capacitor.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features of the present invention, its nature andvarious advantages will become more apparent upon consideration of thefollowing detailed description, taken in conjunction with theaccompanying drawings, in which like reference characters refer to likeparts throughout, and in which:

FIG. 1 is a schematic diagram of an input of an integrated circuitassociated with, for example, an input pin, showing an input resistance,and an input capacitance having fixed and variable components;

FIG. 2A is a graph showing the voltage dependent characteristic of aninput capacitance and the desired characteristic of a compensationcapacitor or circuit;

FIG. 2B is a schematic diagram of a capacitance compensation circuithaving a voltage-dependent input capacitor and a correspondingcompensation capacitor associated with the graph of FIG. 2A;

FIG. 3A is a schematic diagram of a portion of a compensation circuitaccording to the present invention for effecting a linear increase incapacitance with voltage;

FIG. 3B is a graph showing the piece-wise linear compensationcharacteristic associated with the compensation circuit portion shown inFIG. 3A;

FIG. 4A is a schematic diagram of a portion of a compensation circuitaccording to the present invention for effecting a linear decrease incapacitance with voltage;

FIG. 4B is a graph showing the piece-wise linear compensationcharacteristic associated with the compensation circuit portion shown inFIG. 4A;

FIG. 5A is a graph showing the compensation method according to thepresent invention, illustrated in the limit case of both thresholddifferences and incremental capacitors of FIGS. 3A-4B infinitesimallysmall for sake of clarity, in which the combined compensation capacitorcharacteristic is flat with voltage;

FIG. 5B is a graph showing the compensation method according to thepresent invention in the same limit case, in which the combinedcompensation capacitor characteristic is tuned to increase linearly withvoltage;

FIG. 5C is a graph showing the compensation method according to thepresent invention in the same limit case, in which the combinedcompensation capacitor characteristic is tuned to decrease linearly withvoltage;

FIG. 6 is a graph showing the piece-wise linear compensationcharacteristic for effecting an increasing parabolic voltage dependencyin an input capacitor according to the present invention;

FIG. 7 is a graph showing the piece-wise linear compensationcharacteristic for effecting a decreasing parabolic voltage dependencyin an input capacitor according to the present invention;

FIGS. 8A-8C are graphs showing the compensation method according to thepresent invention, illustrated in the limit case of both thresholddifferences and incremental capacitors of FIGS. 3A-4B infinitesimallysmall for sake of clarity, in which the combined compensation capacitorcharacteristic is parabolic and convex;

FIG. 9 is a graph showing the compensation method according to thepresent invention in the same limit case, in which the combinedcompensation capacitor characteristic is parabolic and concave;

FIG. 10 is a first embodiment of a basic two-value comparator+capacitorcircuit suitable for an implementation of the present invention;

FIG. 11 is a second embodiment of a basic two-value comparator+capacitorcircuit suitable for an implementation of the present invention;

FIG. 12 is a first embodiment of a complete continuous-time capacitorcompensation circuit according to the present invention;

FIGS. 13 and 14 are variable-capacitor device (varactor, or varicap)curves associated with the circuit shown in FIG. 12;

FIG. 15 is an alternative embodiment of a tunable comparator+capacitorcircuit suitable for use in a second embodiment of the completecapacitor compensation circuit shown in FIG. 12;

FIG. 16 is a graph of the capacitive characteristic of the alternativeembodiment of a tunable comparator+capacitor circuit shown in FIG. 15;and

FIGS. 17-22 are performance graphs illustrating the various operatingmodes and improvement in performance over the prior art realized withthe circuit and method of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to FIG. 1: an equivalent circuit 100 of a voltage signalapplied to, for example, an input pin of an integrated circuit is shown,where the resistor and capacitors shown can be situated inside, oroutside the chip, or a combination of the two. In the absence of inputresistance, of course the capacitance C_(V) (input-dependent) would beforced to the correct voltage by the input source (V_(SIN), e.g.sinusoidal). However, either a resistance R or capacitor C which arevariable with the voltage imparted across them, can cause the inputsignal to be distorted before reaching the rest of the I.C. (integratedcircuit) 102. Assuming constant resistance R but variable capacitance C,such as:C _(V)(V _(IN))=C _(O)·(1+αV _(IN) +βV _(IN) ²+ . . . )

and noticing that V_(IN)≈V_(S)=A_(O)·sin(ω_(O)·t), by using thefundamental capacitor law:

$i = {\frac{\mathbb{d}q}{\mathbb{d}t} = \frac{\mathbb{d}\left( {C \cdot V} \right)}{\mathbb{d}t}}$$i = {{\frac{\mathbb{d}C}{\mathbb{d}t} \cdot V} + {C \cdot \frac{\mathbb{d}V}{\mathbb{d}t}}}$

and hypothesizing C=C(V):

$i = {{{\frac{\mathbb{d}{C(V)}}{\mathbb{d}V} \cdot \frac{\mathbb{d}V}{\mathbb{d}t} \cdot V} + {{C(V)} \cdot \frac{\mathbb{d}V}{\mathbb{d}t}}} = {\left\lbrack {{\frac{\mathbb{d}C}{\mathbb{d}V} \cdot V} + C} \right\rbrack \cdot \frac{\mathbb{d}V}{\mathbb{d}t}}}$

can be written, where the

$\frac{\mathbb{d}{C(V)}}{\mathbb{d}V} \cdot V$term accounts for the distortion Δi in the current i. The resistor willthen impart a distortion on the ideal sinusoid V_(S) in the amount of afactor R·Δi.

Assuming a quadratic law C(V)=C_(V)(V_(IN)), it is:

$\begin{matrix}{i = {{\left\lbrack {{C_{O} \cdot \left( {\alpha + {2 \cdot \beta \cdot V}} \right) \cdot V} + {C_{O} \cdot \left( {1 + {\alpha \cdot V} + {\beta\; V^{2}}} \right)} +} \right\rbrack \cdot \frac{\mathbb{d}V}{\mathbb{d}t}} =}} \\{= {{\left\lbrack {C_{O} + {C_{O} \cdot \left( {\alpha + \alpha} \right) \cdot V} + {C_{O} \cdot \left( {{2\beta} + \beta} \right) \cdot V^{2}} + \ldots}\mspace{14mu} \right\rbrack \cdot \frac{\mathbb{d}V}{\mathbb{d}t}} =}} \\{= {{C_{O} \cdot \left\lbrack {1 + {2{\alpha \cdot V}} + {3{\beta \cdot V^{2}}} + \ldots}\mspace{14mu} \right\rbrack \cdot \frac{\mathbb{d}V}{\mathbb{d}t}} =}} \\{= {{\underset{\underset{i}{︸}}{C_{O} \cdot \frac{\mathbb{d}V}{\mathbb{d}t}} + \underset{\underset{\Delta\; i}{︸}}{C_{o} \cdot \left\lbrack {{2{\alpha \cdot V}} + {3{\beta \cdot V^{2}}} + \ldots}\mspace{14mu} \right\rbrack \cdot \frac{\mathbb{d}V}{\mathbb{d}t}}} = {\overset{\_}{i} + {\Delta\; i}}}}\end{matrix}$

Since V_(s)(t)=A_(O)·sin(ω₀·t) it is immediate to write:

${\Delta\; i} = {C_{O} \cdot \begin{bmatrix}{{2{\alpha \cdot A_{O} \cdot {\sin\left( {\omega_{0} \cdot t} \right)} \cdot A_{O} \cdot \omega_{O} \cdot {\cos\left( {\omega_{O}t} \right)}}} +} \\{{{+ 3}{\beta \cdot A_{O}^{2} \cdot {\sin^{2}\left( {\omega_{0}t} \right)} \cdot A_{O} \cdot \omega_{O} \cdot {\cos\left( {\omega_{O}t} \right)}}} + \ldots}\end{bmatrix}}$

which, applying the double-angle and Werner trigonometric formulas incascade, yields:

${\Delta\; i} = {{{2 \cdot \alpha \cdot A_{O}^{2} \cdot \omega_{O} \cdot C_{O} \cdot {\frac{\sin\left( {2 \cdot \omega_{O} \cdot t} \right)}{2}++}}3{\beta \cdot A_{O}^{3} \cdot \omega_{O} \cdot C_{O} \cdot \frac{{\cos\left( {\omega_{O}t} \right)} - {\cos\left( {{3 \cdot \omega_{O}}t} \right)}}{4}}} + \ldots}$

highlighting the existence of 2^(nd) and 3^(rd) harmonic terms (HD2 andHD3) due to the C(V) characteristic. Even in presence of an otherwiseideal front-end for an RF or A-to-D conversion subsystem, thevariability of the input capacitance constitutes therefore a limitationto the SFDR performance of the system.

It is desirable to reduce or eliminate the HD2 and HD3 caused by theC(V) dependence, by means of a tunable capacitive compensation circuitthat linearizes the total C(V) characteristic of the input node.

This is shown in FIGS. 2A and 2B, still object of prior art. FIG. 2Breproduces the input circuit 200 including the voltage input signal,input resistance, and variable input capacitor C(V)_(INPUT). Acompensation capacitor C_(COMP) is shown in parallel with C(V)_(INPUT).FIG. 2A shows the capacitance of the voltage-dependent input capacitancewith respect to voltage, the desired capacitance of the compensationcapacitor with respect to voltage, and the total input capacitance,C_(TOT), with respect to voltage. Note that the total input capacitanceis substantially constant with respect to voltage due to thecomplementary shape of the compensation capacitor curve with respect tothe original input capacitance curve.

The desired compensation circuit according to the present invention hasto be able to nullify any value of the α and β coefficients of C_(IN) bysynthesizing a complementary capacitance characteristic featuring −α and−β coefficients. While the amount of C_(O) added to the input node isnot of primary importance (albeit the smallest C_(O) is most desirable),since neither the magnitude nor the sign of the coefficients are known apriori, the widest electrical tunability of α and β is to beaccomplished for their magnitude, and also to yield an additive (+) orsubtractive (−) effect.

The HD2 and HD3 compensation methods and circuits are discussed in turn.

HD2 is eliminated by adding a linear −α·V term to the C_(IN)(V)capacitor. A linear addition, or accumulation, of capacitanceaccomplishes this task in one direction, de facto implementing avoltage-to-capacitance converter. The voltage-to-capacitance converter300 can be construed from prior art and is shown in FIG. 3A, includingthe input terminal VIN, a series of constant thresholds provided byvoltage sources V, a plurality of comparators 302A, 302B, and 302C, aplurality of switches 304A, 304B, and 304C, and a plurality of fixedcapacitors C+. The corresponding piece-wise linear capacitance valueC_(COMP)(V_(IN)) of the additional capacitance versus voltage is shownin FIG. 3B. While three separate stages are shown in FIG. 3A it isobvious to those skilled in the art that additional such stages can beused to achieve any level of granularity desired in the compensatingcapacitance characteristic.

Referring now to FIG. 4A, a single converter stage 400 is shown, whichcan be used in an additional voltage-to-capacitance converter that canalso be construed from prior art for providing an opposite slopedcompensation capacitor. Only one stage is shown, but of course aplurality of any number of such stages can be used. Reverting thepolarity of the comparators 402 leaves all switches 404 “on” forV_(IN)=0V, and progressively opens (“off”) switches 404 as a consequenceof rising V_(IN), which implements a curve shown in FIG. 4B similar tothe one shown in FIG. 3B. Note however that the curve in FIG. 4B issubstantially complementary to the one shown in FIG. 3B. Increasing thenumber of converter stages covering the same input voltage span leads toa shrinking voltage covered by each converter stage, which reduces thegranularity of the C(V) curve and therefore approximates the staircaseprogressively into a single line. By combining both circuits on the sameV_(IN) node, a combined capacitance is realized, as is shown in FIG. 5A.The positive-sloped C+ compensation capacitor and the negative-sloped C−compensation capacitor are combined to form a total compensationcapacitance C_(TOT)(V) that is substantially constant with respect tovoltage.

Of course, if C+>C−, the slope of the rising line is larger than themodulus of the slope of the falling line, and the resultingcharacteristic is slanted in the rising direction as is shown in FIG.5B. If C+<C− then the opposite situation occurs, as is shown in FIG. 5C.The present invention proposes an electrically tunable circuit andmethod to jointly regulate the values of capacitors C+ and C−, hencetuning the “C” component (or, the ordinate axis) of the C(V) curve ofthe complementary capacitor C_(COMP)(V_(IN)). The positive (or negative)slope of the C(V) characteristics is tuned by adjusting C+ versus C−, inorder to maximize the flatness of the total capacitance on the inputnode. A measure of the linearity of the front-end, or of the system as awhole that encompasses the front-end, can be used as figure of merit tosteer the input capacitance balancing process. For lack of directcapacitance measurements, usually extremely challenging when feasible atall, parameters such as the Spurious-Free Dynamic Range (SFDR) of anopamp or an A-to-D converter (ADC), the Integral Non-Linearity (INL) ofan ADC, or the Adjacent Channel Power Ratio (ACPR) in communicationapparata, can be elected as feedback parameters of such tuning process.

The circuit proposed by the present invention can substantially cancelout the linear component of C_(IN)(V), thereby reducing or eliminatingthe term α i.e. the HD2.

As stated by prior art, HD3 can be substantially eliminated by adding aparabolic −βV² term to the C_(IN)(V) capacitor. This quadratic behaviorcan e.g. result from a linear accumulation of progressively increasing(or decreasing) fixed values of C+. Otherwise stated, since the integralof a ramp is a parabola, if:

${\int_{O}^{C}{x \cdot {\mathbb{d}x}}} = {\left\lbrack \frac{x^{2}}{2} \right\rbrack_{O}^{C} = \frac{C^{2}}{2}}$

then instancing a series of linearly scaled capacitors C+, (1+k)·C+,(1+2·k)·C+ leads to a parabolic C_(COMP)(V) profile as shown in FIG. 6,which can be combined with a corresponding arrangement of capacitors C−which are progressively decreasing, starting from the lowest up to thehighest set of comparators/switches as is shown in FIG. 7.

When the number of converter stages is increased, and the granularity isreduced, the two curves combine to yield e.g. a first concave curveshown in FIG. 8A wherein k=j, a second curve shown in FIG. 8B whereink>j, and a third curve shown in FIG. 8C wherein k<j.

When the sign of k and j is inverted, the parabolas have now oppositecurvature, resulting in a convex capacitance profile rather than aconcave profile as is shown in FIG. 9.

It will be apparent to those skilled in the art that yet a higher-orderpolynomial term in the C_(IN)(V_(IN)) characteristic can be compensatedby imparting a quadratic, or cubic, . . . or n-th order progressiveincrease or decrease sequence of the varactor capacitance valuesstarting from the lowest up to the highest set of comparators/switchesas shown in FIG. 7, rather than a linear one.

The present invention proposes an electrically tunable circuit andmethod to jointly regulate the rate of increase (or decrease) ofcapacitors C+ and C− with respect to the sequence of voltage thresholds,by tuning the “C” component of the C(V) curve of the complementarycapacitor C_(COMP)(V_(IN)). The convex (or concave) parabolic curvatureof the C(V) characteristics is modulated by adjusting the rate ofincrease (or decrease) of C+ versus C−, in order to maximize theflatness of the total capacitance on the input node. The tuning methodcan again be configured as a feedback process governed by a figure ofmerit (SFDR, INL peak, ACPR) sensitive to the capacitive-induceddistortion. The proposed circuit arrangement according to the presentinvention can thus also cancel out the parabolic component of C_(IN)(V),reducing or eliminating the term β i.e. the HD3.

It is important to notice that the sequence of voltage values at whichthe capacitance is accumulated maintains a constant step; i.e. thex-axis of all previous figures is linearly exercised; only thecapacitors' values and/or increments are modulated to eliminate α and β.Also, the positive nature of passive capacitors and the accumulationnature of the comparator-stack structure can only lead to a rising rampwhen only a single set of converter stages like those shown in FIG. 3Ais used. To address both positive- and negative-slanted linear inputcapacitance, an additional set of converter stages as shown in FIG. 4Amust be used. Both sets receive the same input voltage V_(IN) at thecorresponding input terminal.

Prior art implementations such as shown in FIG. 3A are functional forlower speeds and for compensating high values of input capacitanceC_(IN). However, obviously it is desirable to devise a mechanism to varyC+, C−, k, and j for tuning out any possible curvature of C_(IN)(V) aspresent in the chip. It is therefore convenient to use variablecapacitors (also known in the art as varactors, or varicaps) to realizeC+ and C−. Also, since the input capacitance of a complete comparatorstructure can easily overwhelm the C_(IN)(V) capacitance and introducenon-linearities of its own, it is desirable to simplify thecomparator+switch structure. For example, in a high-speed bipolarapplication, a fast switching structure like the one shown in FIG. 10 isproposed. Bipolar switching circuit 1000 includes a firstdiode-connected transistor 1002 for receiving the V_(IN) input voltage.A second diode-connected transistor 1004 receives a V_(THRESHOLD1)threshold voltage. The emitters of transistors 1002 and 1004 are coupledtogether and to a tunable capacitor C, which is in turn coupled toground.

With the proper bias, such switching element based on a diode thatengages near V_(THRESHOLD1) can realize the comparator+capacitortopology. A similar concept can be applied to CMOS implementations asshown in circuit 1100 of FIG. 11. In FIG. 11, MOSFET 1102 has a sourcefor receiving the V_(IN) input voltage, a gate for receiving theV_(THRESHOLD1) reference voltage, and a drain coupled to a tunablecapacitor C, which is in turn coupled to ground. Circuit 1100 can beused when a the V_(TH) of a MOSFET can be tolerated as the differencebetween V_(THRESHOLD1) and the input voltage V. The voltage sources ofV_(THRESHOLD1) can then be adjusted to compensate for the V_(TH) of theMOSFETs.

In this respect, notice that a solution that ties the varactor Cdirectly to the switch is indeed more complicated than outlined. Theusage of varactors to give two constant values C+ and C− independentlytunable to correct for α and β is instead implemented as in FIG. 12,where fixed capacitors C_(F) decouple the V_(IN) from the DC voltagedrop across the capacitor. With a fixed voltage on the anode, now theΔV_(HD2) on the cathode modulates the capacitance C of the varactors.

Let us refer in detail to circuit 1200 of FIG. 12, the fullimplementation of a capacitance compensation circuit according to theteachings of the present invention. A first portion of the circuit 1201includes a resistor string 1202 coupled to a plurality of varactors1204. Varactors 1204 are coupled to a plurality of biasing resistors1206 and to a plurality of fixed (“blocking”) C_(B) capacitors 1208.Fixed capacitors 1208 are coupled to the drains of a plurality of PMOStransistors 1212. The gates of the plurality of PMOS transistors 1212are coupled to a resistor string 1210. All the sources of the pluralityof PMOS transistors 1212 are coupled to the input terminal for receivingthe V_(IN) input voltage. The body ties of transistors 1212 are coupledto V_(DD). Resistor string 1202 is biased with two I_(HD3) currentsources, and an additional V_(HD2A) voltage source at the center tap.Resistors 1206 are biased by a V_(HD2C) voltage source, and resistorstring 1210 is biased with the V_(ADJTHp) voltage source. This firstportion provides a compensation capacitance whose linear componentincreases with voltage. The biasing arrangement for the first portion ofcircuit 1200 is explained in further detail below. It will be apparentto those skilled in the art that there are myriad other techniques forgenerating biasing voltages and currents, although a conventionalapproach is shown in FIG. 12.

Continuing to reference FIG. 12, a second portion 1299 of circuit 1200includes a resistor string 1224 coupled to a plurality of varactors1222. Varactors 1222 are coupled to a plurality of biasing resistors1220 and to a plurality of fixed (“blocking”) C_(B) capacitors 1218.Fixed capacitors 1218 are coupled to the drains of a plurality of NMOStransistors 1214. The gates of the plurality of NMOS transistors 1214are coupled to a resistor string 1216. The sources of the plurality ofNMOS transistors 1214 are coupled to the input terminal for receivingthe V_(IN) input voltage. The body ties of transistors 1214 are coupledto ground. Resistor string 1224 is biased with two I_(HD3) currentsources, and an additional V_(HD2A′) voltage source at the center tap.Resistors 1220 are biased by a V_(HD2C′) voltage source, and resistorstring 1216 is biased with the V_(ADJTHn) voltage source. This secondportion provides a compensation capacitance whose linear componentdecreases with voltage. The biasing arrangement for the second portionof circuit 1200 is explained in further detail below. It will beapparent to those skilled in the art that there are myriad othertechniques for generating biasing voltages and currents, although aconventional approach is shown in FIG. 12.

In balanced conditions of operation, the current I_(HD3)=0 and allvaractors of sets 1204 and 1222 are biased with the same voltageV_(var)=V_(HD2A)−V_(HD2C)=V_(HD2A′)−V_(HD2C′) across them, producinglinearly increasing and decreasing C(V) characteristics that add up to aflat overall C_(COMP)(V_(IN)) profile. An imbalance in V_(HD2A)−V_(HD2C)versus V_(HD2A′)−V_(HD2C′) will privilege one slope versus the other,synthesizing—as allowed by the linearity of the varactor devices—alinear slant in the overall C_(COMP)(V_(IN)). Activating a I_(HD3)≠0current will instead engender a linear gradient in the values of thevaractors' capacitances, out of phase in the two opposite halves of FIG.12, and ultimately a concave or convex curvature modification in theoverall C_(COMP)(V_(IN)).

Since C_(B)//C_(varactor) yields the effective C_(IN) correction,usually designing for a large C_(B)>>C_(varactor) improves thesensitivity. Notice that C_(B) can be progressively scaled to compensatefor the body effect of the switches and consequently compensate for thisx-axis distortion, if the MOSFET bulk is not otherwise driven. Analogousmeasure can be taken by biasing the bulk progressively higher forNMOSFETs that are triggered at higher V_(IN), by way of example, withanother string of identical or scaled resistors.

In presence of a C(V) timing characteristic of a p-n junction varactorof the type:

${C\left( V_{var} \right)} = \frac{C_{0}}{\sqrt[m]{1 - \frac{V_{var}}{\phi_{bi}}}}$

where m=2÷3 and φ_(bi) is the built-in voltage of the junction, theC_(VAR) curve is given in FIG. 13.

The capacitor curve shown in FIG. 13 is used to modify HD2 throughadjustments of the differential potential V_(var)=V_(HD2A)−V_(HD2C).

The previous arrangement also allows for implementing the HD3correction. When a set of cathode voltages V_(HD2A)±nR·I_(HD3) isestablished on the varactors, a set of increasing capacitance values C+or C− is obtained, and a parabolic C_(COMP)(V_(IN)) profile is obtained.Of course, the non-linearity of the C_(VAR) curve induces deviationsfrom the ideal parabolic profile onto C_(COMP)(V_(IN)). Rather than anideal ohmic drop nR·I_(HD3) some non-linear arrangement of resistors canbe devised to equalize such C_(VAR) curve. Another solution to this lastproblem is to use an MOS capacitor, best in accumulation rather than ininversion, and exploit the better linearity of their C_(VAR) curve inthe vicinity of the V_(FLAT-BAND): as is shown in FIG. 14.

The linear region of the C_(VAR) characteristic is only achieved over anarrow band of adjustment voltages (currently 1 to 2V) but allows theHD3 correction by way of a simple resistor string. Also, in this caseany forward-biasing of the p-n junctions is avoided in this case. It isalso possible to avoid this phenomenon even with traditional varactors,owing to the flexibility of setting V_(HD2A)−V_(HD2C) at will. Noticethat biasing the MOSFET varactor in either of the “forbidden” flatregions would entail the loss of tunability of the structure, which atthat point would correct only for one magnitude of HD2; and, have noeffect on HD3.

Notice how the direct coupling of the varactor device to the input couldforward-bias the diode, if a p-n implementation was chosen; but even inthe MOS case, the variable capacitance C_(VAR) would in such case bemodulated not only by a V_(HD2A)−V_(HD2C)−nR·I_(HD3) constant voltage,but also by the V_(IN) input voltage. One side of the varactor is goingto be connected to V_(IN) only when the corresponding switch turns “on”.This makes the circuit V_(TH)-dependent and thus more sensitive toprocess, temperature, and potentially to other phenomena such asradiation-induced discharge. Also, the asymmetry between the side of thecircuit using NMOSFETs (to decrease capacitance with rising V_(IN)) andPMOSFETs (to increase capacitance with rising V_(IN)) causes a skew ofapproximately V_(Thn)+|V_(THp)| which has to be adjusted by shifting,the voltage on the opposite electrode of the varactor: a necessity thatinterferes with the voltage level tuning for sake of HD2 and HD3correction. The adoption of blocking capacitors to maintain a wellcontrolled voltage across the varactors greatly relieves these issuesand enables a more precise fine-tuning of their values.

An additional solution making use of a MOSFET varactor in lieu of theMOSFET switch, where the on/off values of the CMOSFET in series with ap-n or MOS varactor is used as a capacitance switching mechanism, canalso be envisioned. A realization of a branch of such alternativecircuit 1500 is shown in FIG. 15. Circuit 1500 includes a first varactorcoupled between the input terminal and an intermediate node 1508, and asecond varactors coupled between intermediate node 1508 and center tapnode 1510. A resistor 1502 is coupled between intermediate node 1508 andan adjust voltage VHD2C. The center tap or biasing voltage 1510 isprovided by a resistor string, analogous to 1202 in FIG. 12. Onlyresistors 1504 and 1506 of the resistor string are depicted.

The circuit 1500 shown in FIG. 15 modulates the C_(VAR)//C_(SWITCH) bymaking use of the “saturated” C_(SWITCH) characteristic as is shown inFIG. 16. As can be seen, circuit 1500 can yield a very smooth and linearC(V) characteristics. However, this implementation suffers fromdrawbacks such as:

-   -   C_(SWITCH) “on” is not constant, but varies, due to poly-gate        depletion mechanisms, and this is enough to modulate the        C_(COMP)(V_(IN)) as a whole; and    -   since the series C_(SWITCH)//C_(VAR) is used, now        C_(SWITCH)≡C_(P) can no longer be >>C_(VAR). In fact, the        C_(SWITCH ON)/C_(SWITCH OFF) ratio is only 5:1 at the most, and        this limits the tunability of the circuit as a whole.

The circuits and embodiments of the present invention presents a“piece-wise linear” C_(COMP)(V_(IN)) characteristic, due to the presenceof switches (or, comparators). Increasing the number of comparisonthresholds improves the granularity of the circuit, reducing thesuper-harmonics generated by the invention. However, the solutionproposed by the present invention does not require buffering,level-shifting, or input re-sampling. It can be therefore directlycoupled to the RF or analog precision input in continuous time, therebycompensating the continuous-time C_(IN)(V_(IN)) at each instant, withnegligible phase delay for frequencies up to the GHz.

FIGS. 17-22 are performance graphs illustrating the various operatingmodes and improvement in performance over the prior art realized withthe circuit and method of the present invention.

FIG. 17 shows the case when the embodiment of the invention depicted inFIG. 12 is operated in a balanced condition, in which the value of thevaractors in sets 1204 and 1222 is made identical by imparting the samepotential difference V_(HD2A)−V_(HD2C)=V_(HD2A′)−V_(HD2C′) on both, withI_(HD3)=0. Since the positive and negative slopes of the C(V) of bothhalves of FIG. 12 are identical and no curvature is imparted, the totalcompensation capacitance seen at the input terminal is flat againstV_(IN) at about 190 fF. Higher or lower capacitance values can besynthesized by instancing larger or smaller devices in the physicalimplementation of the circuit.

FIG. 18 shows a case when the embodiment of the invention depicted inFIG. 12 is operated to provide HD2 cancellation. The value of thevaractors in set 1204 is driven lower than the value of set 1222 byimparting a potential difference V_(HD2A)−V_(HD2C)<V_(HD2A′)−V_(HD2C′),while keeping I_(HD3)=0. Since the positive C(V) slope synthesized byset 1204 is exceeded by the negative C(V) slope synthesized by set 1222and no curvature is imparted, the total compensation capacitance seen atthe input terminal is linearly decreasing against V_(IN).

FIG. 19 shows an alternative case when the embodiment of the inventiondepicted in FIG. 12 is operated to provide HD2 cancellation. The valueof the varactors in set 1204 is driven higher than the value of set 1222by imparting a potential differenceV_(HD2A)−V_(HD2C)>V_(HD2A′)−V_(HD2C′), while keeping I_(HD3)=0. Sincethe positive C(V) slope synthesized by set 1204 exceeds the negativeC(V) slope synthesized by set 1222 and no curvature is imparted, thetotal compensation capacitance seen at the input terminal is linearlyincreasing against V_(IN).

FIG. 20 shows a case when the embodiment of the invention depicted inFIG. 12 is operated to provide HD3 cancellation. The decrement (forincreasing V_(IN)) in the value of the varactors in set 1204 is opposedto the increment in the value of the varactors in set 1222 by keeping apotential difference V_(HD2A)−V_(HD2C)=V_(HD2A′)−V_(HD2C′), whileimparting negative I_(HD3) on the 1202 and positive I_(HD3) on the 1224branches. Since the convex C(V) curvature synthesized by set 1204 iscombined with the convex C(V) curvature synthesized by set 1222, thetotal compensation capacitance seen at the input terminal is convexagainst V_(IN). The residual linear slope is a byproduct of thecombination of the two parabolae and can be eliminated with thetechnique previously described, if so desired.

FIG. 21 shows an alternative case when the embodiment of the inventiondepicted in FIG. 12 is operated to provide HD3 cancellation. Theincrement (for increasing V_(IN)) in the value of the varactors in set1204 is opposed to the decrement in the value of the varactors in set1222 by keeping a potential differenceV_(HD2A)−V_(HD2C)=V_(HD2A′)−V_(HD2C′), while imparting positive I_(HD3)on the 1202 and negative I_(HD3) on the 1224 branches. Since the concaveC(V) curvature synthesized by set 1204 is combined with the concave C(V)curvature synthesized by set 1222, the total compensation capacitanceseen at the input terminal is concave against V_(IN). The residuallinear slope is a byproduct of the combination of the two parabolae andcan be eliminated with the technique previously described, if sodesired.

FIG. 22 finally shows the AC capacitive results, in which a frequencysweep of the value of the total capacitance seen at the input of theembodiment of FIG. 12 is reported. The typical I∝ωC_(COMP) behavior ofthe AC current plot highlights the broad range of frequency in which thecircuit acts as a capacitor. The variable current level observed againsta sweep of V_(IN) reflects the capacitance modulation C_(COMP)(V_(IN)),which returns figures such as FIGS. 17-22 when plotted against theV_(IN) value itself.

Although the invention has been described and illustrated with a certaindegree of particularity, it is understood that the present disclosurehas been made only by way of example, and that numerous changes in thecombination and arrangement of parts can be resorted to by those skilledin the art without departing from the spirit and scope of the invention,as hereinafter claimed.

1. A capacitance compensation circuit comprising: an input terminal; acircuit to compensate for input capacitance increasing against the inputterminal voltage, comprising a first plurality of switches coupled tothe input terminal, a first plurality of blocking capacitors coupled tothe first plurality of switches, and a first plurality of varactorscoupled to the plurality of blocking capacitors; and a circuit tocompensate for input capacitance decreasing against the input terminalvoltage, comprising a second plurality of switches coupled to the inputterminal, a second plurality of blocking capacitors coupled to thesecond plurality of switches, and a second plurality of varactorscoupled to the second plurality of blocking capacitors.
 2. Thecapacitance compensation circuit of claim 1 wherein the first pluralityof switches comprises a plurality of devices inactivated by a switchingvoltage thereof exceeding a threshold voltage.
 3. The capacitancecompensation circuit of claim 1 wherein the second plurality of switchescomprises a plurality of devices activated by a switching voltagethereof exceeding a threshold voltage.
 4. The capacitance compensationcircuit of claim 1 further comprising: a first plurality of bias levelscoupled to a plurality of control terminals associated with the firstplurality of switches; and a second plurality of bias levels coupled toa plurality of control terminals associated with the second plurality ofswitches.
 5. The capacitance compensation circuit of claim 4 wherein:the first plurality of bias levels comprises a first plurality ofconstant bias levels; and the second plurality of bias levels comprisesa second plurality of constant bias levels.
 6. The capacitancecompensation circuit of claim 1 further comprising: a first plurality ofbias devices coupled to the first plurality of blocking capacitors; anda second plurality of bias devices coupled to the second plurality ofblocking capacitors.
 7. The capacitance compensation circuit of claim 6further comprising: a first adjustable source coupled to the firstplurality of bias devices; and a second adjustable source coupled to thesecond plurality of bias devices.
 8. The capacitance compensationcircuit of claim 1 further comprising: a first plurality of adjustablebias levels coupled to the first plurality of varactors; and a secondplurality of adjustable bias levels coupled to the second plurality ofvaractors.
 9. The capacitance non-linearity compensation circuit ofclaim 8 further comprising: a first adjustable bias source to similarlyadjust the capacitance of each varactor in the first plurality ofvaractors; and a second adjustable bias source to similarly adjust thecapacitance of each varactor in the second plurality of varactors. 10.The capacitance non-linearity compensation circuit of claim 8 furthercomprising: a first adjustable bias source to linearly adjust thecapacitance of consecutive varactors in the first plurality ofvaractors; and a second adjustable bias source to linearly adjust thecapacitance of consecutive varactors in the second plurality ofvaractors.
 11. The capacitance compensation circuit of claim 1 whereinthe first and second plurality of varactors each comprise a plurality ofMOS varactors.
 12. The capacitance compensation circuit of claim 1wherein the first and second plurality of varactors each comprise aplurality of p-n junction varactors.